Herald of Kazakh-British technical university

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1998-6688

2959-8109

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ON THE APPROXIMATION OF A BOUNDARY VALUE PROBLEM FOR DELAY INTEGRO-DIFFERENTIAL EQUATIONS
(2025-07-06)
E. А. Bakirova
;
Narkesh B. Iskakova
;
Askarbek E. Imanchiyev
;
Sayakhat G. Karakenova
A linear two-point boundary value problem for a system of integro-differential equations with a constant delay argument is investigated on a finite interval. By dividing the interval by parts, the integral term of the integrodifferential equation with constant delay argument is replaced by the quadrature formula. With this replacement, the linear two-point boundary value problem for a system of integro-differential equations with a constant delay argument is approximated by the linear boundary value problem for a system of loaded differential equations with a constant delay argument. Definitions of correct solvability of boundary value problem for system of integro-differential equations with delay argument and constructed boundary value problem for system of loaded differential equations with constant delay argument are introduced. Conditions of correct solvability of linear boundary value problem for system of integro-differential equations with delay argument and linear boundary value problem for system of loaded differential equations with delay argument are established. Relationship between correct solvabilities of linear two-point boundary value problem for system of integro-differential equations with constant delay argument and approximating linear two-point boundary value problem for system of loaded differential equations with constant delay argument is shown.
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ON THE SOLUTION OF A BOUNDARY VALUE PROBLEM FOR AN IMPULSIVE HYPERBOLIC EQUATION WITH A PIECEWISE-CONSTANT ARGUMENT
(2026-06-27)
Altynai Molybaikyzy
;
Symbat Seisenbekovna Kabdrakhova
;
Narkesh B. Iskakova
;
B. B. Мinglibayeva
This article investigates a boundary value problem for an impulsive hyperbolic equation with a piecewise constant argument. Impulsive hyperbolic equations with a piecewise constant argument arise as mathematical models of physical processes in neural networks, continuous dynamical systems, hybrid systems, and other fields. Issues related to the existence of boundary value problems and the construction of their solutions for such equations remain among the most relevant and challenging problems at present. To obtain solvability conditions for the considered problem, the Dzhumabaev parametrization method is employed, and an iterative algorithm for constructing an approximate solution is developed. For each step of the iterative process, integral formulas are derived and expressed in terms of the matrix Q(x), which describes the relationship between the functional parameters. If this matrix is invertible, the existence and uniqueness of the solution are proved both for the parametric and the original problems. The proposed method is not limited to proving theoretical solvability; it also provides a concrete constructive procedure for obtaining the solution. This is of significant importance for subsequent numerical implementations and for the analysis of solution stability. Moreover, the proposed approach can be applied to other types of problems with a piecewise constant argument, including systems with impulsive conditions, neural networks with memory effects, and nonlinear hybrid models.
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MATHEMATICAL THEORY OF THE INCLINED PLANE
(2024-03-26)
Т. Б. Қоштыбаев
;
Kutkeldiyeva Elzira
;
К. К. Жантлеуов
;
E. Zhamenkeev
The laws of mutual transformation of statistical and dynamic effects on an inclined plane are shown, a mathematical justification is given for obtaining a gain from the action or the possibility of saving the main useful action and facilitating the actions of Gravity. All the above statements are carried out using the basic elements of the theories of dynamics, statics and trigonometric calculations. The influence of the geometric dimensions of the inclined plane on the transformation of actions is estimated. The mechanism of statistical and dynamic equilibrium of actions on an inclined plane is substantiated through mathematical expressions of the conservation law and the relationship between the components of the vector.
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MICRO- AND NANOMICROMATERIALS IN PYROTECHNICS
(2024-07-02)
Zh.K. Aimasheva
;
Д. В. Исмаилов
;
Valentina Grichshenko
;
Stefano Bellucci
;
Г. Партизан
Due to their unique physical and chemical properties, which play an unrivaled role in enhancing the performance and safety of pyrotechnic substances, carbon nanomaterials have garnered significant interest from researchers in recent years. In this paper, carbon nanostructures prepared by electric arc synthesis are identified as C60 and C70 fullerene carbon blacks. The carbon black particles derived from the synthesized fullerenes exhibit a porous and rough morphology, with sizes ranging from 32 to 190 nm. The experimental results indicate the potential use of synthesized fullerene soot as a constituent component of pyrotechnic composites. The dependence of pyrotechnic composite compositions on combustion time has been determined by selecting potassium nitrate, nanoscale fullerenes, composite carbon blacks, wood coals, and aluminum fillers as matrix materials. According to the findings, the combustion time of the composite composition increases as the content of fullerene soot in the pyrotechnic composite composition increases.
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NUMERICAL SOLUTION OF A BOUNDARY VALUE PROBLEM WITH A PARAMETER FOR IMPULSIVE LOADED DIFFERENTIAL EQUATIONS
(2024-07-01)
Zh. М. Каdirbayeva
;
Svetlana Temesheva
;
B. B. Мinglibayeva
;
N. M. Shaimerden
The boundary value problem depending on the parameter for the system of impulsive loaded differential equations is considered. Algorithms of numerical realization of the Dzhumabaev parameterization method are developed for numerical solving of the studied boundary value problem depending on the parameter. Algorithms of numerical realization of the Dzhumabaev parameterization method are based on the solving of Cauchy problems for the system of ordinary differential equations. As a result of application of the proposed method, finding a solution to the boundary value problem depending on the parameter for impulsive loaded differential equations leads to finding a solution to the system of algebraic equations. This system of algebraic equations consists of a boundary condition and equalities with respect to the conditions at the impulsive points. Numerical results showing the high efficiency of the numerical implementation of the Dzhumabaev parameterization method are given. The result demonstrate that there is congruence between the numerical and the exact results to a high order of accuracy.
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ON A BOUNDARY VALUE PROBLEM FOR HIGH-ORDER HYPERBOLIC EQUATION WITH IMPULSE DISCRETE MEMORY
(2024-10-02)
A. T. Assanova
;
R. A. Bimenova
;
B. B. Мinglibayeva
;
A. P. Sabalakhova
The investigation focuses on a boundary value problem for a high-order hyperbolic equation with impulse discrete memory in a rectangular domain. By introducing new functions, the problem is transformed into a set of boundary value problems for a first-order differential equation with impulse discrete memory, which depends on unknown functions and integral relations. D.S. Dzhumabaev's parametrization method is applied to this equivalent problem. The domain is divided according to the time variable, and functional parameters representing discrete memory values are introduced within the interior domains. As a result, the family of boundary value problems for the first-order differential equation with impulse discrete memory and unknown functions is converted into an equivalent family of integral-multipoint boundary value problems involving functional parameters and unknown functions. These equivalent problems include initial value problems for first-order differential equations related to the new functions. The solutions to the initial value problems are expressed using Volterra integral equations. By substituting these solutions into the boundary and impulse conditions, a system of linear functional equations concerning the functional parameters is derived. An algorithm is developed to solve the equivalent problem, and sufficient conditions for the unique solvability of the family of integral-multipoint boundary value problems with functional parameters and unknown functions are provided. Additionally, sufficient conditions for the unique solvability of the original boundary value problem for the high-order hyperbolic equation with impulse discrete memory are established based on the initial data.
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KINEMATICS AND STRUCTURE OF THE MASSIVE STAR-FORMING REGION G350.29+0.12
(2026-03-29)
Aidana Abdirakhman
;
Aruzhan Omar
;
Zhomartkali Islyam
;
N.Sh. Alimgazinova
;
Aizat Demessinova
We present high–angular resolution 1.3 mm continuum and molecular line observations toward the highmass star-forming region G350.29+0.12, using CH₃CN and CH₃¹³CN rotational transitions. The continuum emission resolves two main cores: a bright, compact northern core G350.29+0.12 A and a weaker southern core G350.29+0.12 B. Core A exhibits six compact substructures embedded within more extended emission. M K-components of the CH3CN J = 14→13 and CH3 13CN J = 14→13 transitions are detected, with the emission arising primarily from core A. The CH3CN moment 0 maps show that the integrated intensities peak at the main continuum position, indicating that the molecular emission traces warm and dense gas. The moment 1 maps reveal a pronounced velocity gradient of ∼2 km s-1 across core A, oriented from northwest to southeast, while the moment 2 maps show K-dependent variations in velocity dispersion. Position–velocity diagrams further indicate organized rotational motions, exhibiting a compact velocity structure with a central peak and systematic gradients. Rotational temperature analysis yields = 360.6 ± 34.8 K for CH3CN, tracing the hottest and densest gas and Trot = 138 ± 45 K for CH3 13CN, consistent with cooler and more extended material. Together, these results demonstrate that G350.29+0.12 A is a rotating hot molecular core undergoing active high-mass star formation.
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NUMERICAL STUDY OF ORBITAL STABILITY IN THE RELATIVISTIC RESTRICTED THREE-BODY PROBLEM
(2026-03-29)
Ayazhan Orazymbet
;
Aliya Taukenova
;
Daniya Utepova
;
Nurzada Beissen
;
N. Sandibayeva
This paper presents a numerical study of the relativistic restricted three-body problem within the framework of General Relativity. Using the Lagrangian and Hamiltonian formalisms, the equations of motion with relativistic corrections up to the order of 1/c2 were derived and solved numerically in Wolfram Mathematica. The developed model allows one to analyze orbital stability under small relativistic perturbations. Numerical simulations were performed using the Runge–Kutta integration method for three systems: “Earth–Sun–Moon,” “Earth–Sun– Mercury,” and an equal-mass configuration. The results confirm the stability of circular orbits and reproduce the observed relativistic precession of Mercury’s perihelion. For the equal-mass system, the calculations reveal a transition from quasi-periodic to chaotic motion, depending on the initial conditions. The study demonstrates the reliability and efficiency of the Mathematica environment for modeling nonlinear relativistic dynamics and shows that the proposed approach can be useful for further research in celestial mechanics and gravitational physics.
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COMPARATIVE ANALYSIS OF X-RAY LUMINOSITY OF PERSISTENT AND TRANSIENT HIGH-MASS X-RAY BINARIES
(2026-03-29)
Zhantay Muratkhan
;
Manas Khassanov
;
Aray Muratkhan
;
Aliya Taukenova
;
A. Sadu
High-mass X-ray binaries (HMXBs) are commonly divided into persistent sources, which emit X-rays steadily over long periods, and transient sources, which remain mostly in a quiescent state and exhibit episodic X-ray outbursts. The aim of this work is to statistically compare the X-ray luminosity properties of these two classes, focusing on the maximum luminosity and the luminosity variability range . For this purpose, catalog data for Galactic HMXB pulsars were used, including 18 persistent and 64 transient systems. The distributions of and were analyzed using histograms, box plots, cumulative distribution functions (CDFs), and the non-parametric Mann–Whitney test. It is shown that both classes reach similar values of on the order of – erg/s), with no statistically significant difference between their distributions. However, transient systems exhibit a much wider luminosity variability range, reaching increases of 4–5 orders of magnitude (up to ), whereas persistent sources typically show lower variability. This difference is statistically confirmed, with transients demonstrating significantly higher variability p ≈ 0.05). Thus, the main distinction between persistent and transient HMXBs lies not in their peak X-ray luminosity, but in their accretion regime. In persistent systems, the compact object continuously accretes matter from a relatively stable stellar wind of an OB supergiant, resulting in steady X-ray emission. In contrast, transient systems are characterized by intermittent accretion (for example, episodic mass capture from a Be-star circumstellar disc), which leads to their extreme luminosity variability.
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STUDY OF THE W40 STAR-FORMING REGION BASED ON OBSERVATIONS BY THE WISE INFRARED SPACE TELESCOPE
(2026-03-29)
N.Sh. Alimgazinova
;
A.B. Manapbayeva
;
Aruzhan Omar
;
Aizat Demessinova
;
Kunduz M. Turekhanova
The study of the mechanisms of star formation and evolution is based on comprehensive research into interstellar regions, including the analysis and identification of young stellar objects (YSOs). The identification of young stellar objects by their radiation at various wavelengths in the infrared range is a relatively recent development - the first studies in this field appeared only at the end of the 20th century. The development of this field has been made possible by improvements in observation techniques and data processing methods, the acquisition of more reliable characteristics of stellar sources, and the creation of catalogs containing extensive arrays of information about cosmic objects. In this study, the star-forming region W40 of the Aquilla molecular cloud was investigated in the infrared wavelength range to detect previously unidentified young stellar objects at various stages of evolution. Identification was carried out using two approaches: photometric criteria and spectral indices. This made it possible to more reliably identify the evolutionary stages of 37 newly discovered and previously unexplored YSO candidates (5 objects of class I, 2 objects of class II, 4 objects – class “transitional disks” and 26 objects — class III), which indicates an active and ongoing process of star formation in W40.

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